Chapter 12.7, Problem 5CYU

(a)

To determine

To Find: The graph for the binomial probability distribution.

Answer to Problem 5CYU

The required graph is shown in Figure 2

Explanation of Solution

Calculation:

Consider $x$ is the random variable that show the number of student where in favour of the expanding of the junior parking lot. Where x is the binomial distribution with the parameters $n=6$ and $s=0.85$ .

Then, the probability distribution function of $x$ is,

  $\begin{array}{c}P\left(X=x\right)=\left(\begin{array}{c}6\\ x\end{array}\right){\left(0.85\right)}^x{\left(1-0.85\right)}^{6-x}\\ =\left(\begin{array}{c}6\\ x\end{array}\right){\left(0.85\right)}^x{\left(0.15\right)}^{6-x}\end{array}$

The table for probability for all the value of $x$ is shown in Table 1

Table 1

X	$P\left(X=x\right)$
0	0.000
1	0.004
2	0.0055
3	0.0415
4	0.1762
5	0.3993
6	0.3771

The required graph is shown in Figure 2

  

Figure 2

(b)

To determine

To Find: The probability that all the 6 of the students were in favour of expansion.

Answer to Problem 5CYU

The required probability is $0.3771$ .

Explanation of Solution

Calculation:

The probability that all the 6 of the students were in favour of the expansion is,

  $\begin{array}{c}P\left(X=x\right)=\left(\begin{array}{c}6\\ 6\end{array}\right){\left(0.85\right)}^6{\left(0.15\right)}^{6-6}\\ =0.3771\end{array}$

The required probability is $0.3771$ .